Diffraction by a disk

Abstract

The problems of diffraction of sound waves by a perfectly ‘soft’ and a perfectly rigid circular disk are studied. An arbitrary non-axially symmetric wave is assumed to be incident on the disk. It is shown that both problems can be reduced to the solution of Fred­holm integral equations of the second kind. The method of solution seems to be new and does not involve the solving of sets of simultaneous linear equations. The present approach may also be applied to the solution of other problems such as the transmission of waves through circular holes in parallel screens. The kernels of the integral equations are reasonably elementary functions, and the equations are particularly suitable for obtaining iterative approximate solutions at low frequencies. The special case of an incident plane wave is considered in detail and expansions in powers of (frequency x radius) are obtained for the respective transmission coefficients.